New York City neighborhood more or less bounded (there isn't an official division - even NYC's official neighborhood map, referenced below, is deliberately vague) by
34th street to the north 26th street to the north, 14th street to the south, Lexington Avenue to the west and the East River to the east. Named after Gramercy Park, a private park at the bottom of Lexington Avenue at 21st street.
The area is charming, full of converted stone tenements, chinese laundries, tons of food (cheap and not so cheap) of all kinds. The population is quite young, probably because a good portion of the affordable apartments in the area are one bedroom or smaller: lots of people under thirty, middle to upper middle class, mostly childless, students or recent former students.
This gets to the heart of what makes Gramercy so awsome, at least to me: with the exception of the fast food joints that are everywhere, the neighborhood seems to have been totally ignored by the big chains (if you're a marketing director and are reading this, stay away). The closest Gap is on 14th street. The neighborhood does have a starbucks infection, but only two locations (if you've been to New York you'll understand how rare that is - this is the town where you can find two Starbucks directly across the street from each other).
We've got other stuff. 23rd street is goodwill central: thrift stores, New York housing works, the Salvation Army. Third avenue is packed with bars, sushi and coffee houses. The bagels will blow you away. The river is right there (it's easy to forget that Manhattan is an island sometimes) with an awsome view of Brooklyn. The School of Visual Arts and Baruch are here. There's a tiny little brick park across the street from my apartment, sandwiched between an apartment building and a Duane Reade, with an honest to god art deco fountain in it; you'd never know existed if you didn't hear the running water.
Transportation is a bit of a pain, but manageable - the 6 train stops at 23rd and 28th streets and Park Avenue South, and the Union Square megastation isn't far. MTA busses run crosstown on 23rd and 34th, and uptown and downtown on all the avenues.
In recent years a new neighborhood has been taking shape to the north, around 34th street from Third Avenue to the East River: Kips Bay. It's a bit grittier, a bit more commercial, yet still embracing the same attributes that make Gramercy so comfortable.
Map info taken from http://www.nyc.gov/html/dcp/html/neighbor/neigh.html
The rest is from experience.